Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts
Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts
复制标题
DOI：
10.1063/1.5108665
复制
发表时间：
2019-05
影响因子：
4.6
通讯作者：
S. Jaiswal;Aaron Pikus;A. Strongrich;I. Sebastião;Jingwei Hu;Alina A. Alexeenko
中科院分区：
文献类型：
--
作者：
S. Jaiswal;Aaron Pikus;A. Strongrich;I. Sebastião;Jingwei Hu;Alina A. Alexeenko
当流动足够稀薄时，温度梯度，例如，被几个平均自由程分开的两壁之间的温度梯度，就会诱导气体流动-这种观察归因于微尺度上的热应力对流效应。整个热应力对流过程的动力学由Boltzmann方程控制-描述分子分布函数在六维相空间中的演化的积分-微分方程式-它在分子水平上模拟稀释气体的行为，以准确地描述广泛的流动现象。求解具有一般分子间相互作用的完整Boltzmann方程的方法依赖于两种观点：一种是随机的，通常采用直接模拟蒙特卡罗(DSMC)方法；另一种是确定性的。在确定性方法中，不连续Galerkin快速谱(DGFS)方法最近被引入来求解具有一般碰撞核的完整Boltzmann方程，其中包括模拟扩散输运流动所必需的可变硬/软球模型。本文利用确定性DGFS方法、Bhatnagar-Gross-Krook(BGK)、椭球统计BGK和Shakhov动力学模型，以及广泛使用的随机DSMMC方法，对微型面内克努森辐射致动器MIKRA中的热应力对流过程进行了研究。BGK模型对热流密度、剪应力和流速的预测偏低，S模型对热流密度、剪应力和流速的预测偏高，而ESBGK模型的预测结果与数值模拟结果较为接近。另一方面，无论是统计/DSMMC方法还是确定性/DGFS方法，在视角上都是分开的，但都会产生难以解决的结果。
When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow---an observation attributed to the thermo-stress convection effects at microscale. The dynamics of the overall thermo-stress convection process is governed by the Boltzmann equation---an integro-differential equation describing the evolution of the molecular distribution function in six-dimensional phase space---which models dilute gas behavior at the molecular level to accurately describe a wide range of flow phenomena. Approaches for solving the full Boltzmann equation with general inter-molecular interactions rely on two perspectives: one stochastic in nature often delegated to the direct simulation Monte Carlo (DSMC) method; and the others deterministic by virtue. Among the deterministic approaches, the discontinuous Galerkin fast spectral (DGFS) method has been recently introduced for solving the full Boltzmann equation with general collision kernels, including the variable hard/soft sphere models---necessary for simulating flows involving diffusive transport. In this work, the deterministic DGFS method; Bhatnagar-Gross-Krook (BGK), Ellipsoidal statistical BGK, and Shakhov kinetic models; and the widely-used stochastic DSMC method, are utilized to assess the thermo-stress convection process in MIKRA---Micro In-Plane Knudsen Radiometric Actuator---a microscale compact low-power pressure sensor utilizing the Knudsen forces. BGK model under-predicts the heat-flux, shear-stress, and flow speed; S-model over-predicts; whereas ESBGK comes close to the DSMC results. On the other hand, both the statistical/DSMC and deterministic/DGFS methods, segregated in perspectives, yet, yield inextricable results.